基于高效NMPC算法的无人车轨迹跟踪控制研究

doi:10.19562/j.chinasae.qcgc.2022.10.003

Abstract

Abstract:

In view of the lowering of the trajectory tracking accuracy and the solution efficiency caused by the increase of nonlinear degree and dynamic constraints of unmanned vehicles under complex working conditions， an efficient algorithm based on nonlinear model predictive control （NMPC） is proposed in this paper. Firstly， in consideration of the nonlinear factors of the vehicle model， the dynamic model and the magic formula tire model are established. A terminal state is integrated to the performance index. The multi-constraint conditions within the stability range are added， and barrier function method is used to solve nonlinear inequality constraints to ensure the smoothness of the solution process. Then in order to reduce the computational burden caused by solving nonlinear optimization problems， an improved continuous/generalized minimum residual （improved-C/GMRES） algorithm is proposed. Compared with the traditional C/GMRES algorithm， the continuously increasing penalty factor is introduced to speed up the numerical calculation efficiency and reduce the computational burden of the algorithm. Finally， based on the joint simulation platform of Simulink and Carsim， the trajectory tracking accuracy and solution efficiency are verified in double-shift line motion and serpentine motion. Simulation results show that compared with the traditional C/GMRES algorithm， the proposed algorithm can significantly improve the tracking accuracy and driving stability of trajectory tracking， and greatly accelerates the solution efficiency.

Key words: unmanned vehicle, trajectory tracking, nonlinear model predictive control, improved-C/GMRES, solution efficiency

Hongwei Wang,Chenyu Liu,Lei Li,Haotian Zhang. Research on Trajectory Tracking Control of Unmanned Vehicle Based on Efficient NMPC Algorithm[J].Automotive Engineering, 2022, 44(10): 1494-1502.

Figures/Tables 18

步骤

C/GMRES算法

步骤1

输入 $t = 0$ ， $x 0 = x (0)$ ， $Δ t = 0.05$ ， $Δ x = 0$ ；

寻找满足 $F (U, x (t), ε) ≤ ?$ 的初始序列 $U (0)$

步骤2

当

t ∈ [t, t + T]

，将控制序列的第一个元素作为实际控制输入，即

u (t) = u 0 * (t)

步骤3

当 $t ∈ [t, t + T]$ ，令 $U (t) = U (t - Δ t)$ ；

$x 0 = x (t)$ ， $Δ x = x (t) - x (t - Δ t)$ ；

$x ˙ (t) = Δ x / Δ t$ ；

$U ˉ ˙ = F D G M R E S (U, x (t), x ˙ (t), t, U ?, η m a x, ε)$

$U * = U d + U ˉ ˙ ? Δ l$ ；返回步骤2

步骤	improved-C/GMRES算法
步骤1	输入 $d = 0$ ， $ε 0 = 0.1$ ， $Δ t = 0.05$ ， $Δ x = 0$ ， $U ? - 1 = 0$ ， $x 0 = x (0)$ ，增量系数 $ρ = 10$ ，最大迭代次数 $d m a x = 11$ ；初始化寻找满足条件 $F (U, x (t), ε) ≤ ?$ 的初始控制输入序列 $U 0$ ，其中 $?$ 为正实数。
步骤2	当 $d ≤ d m a x$ 时， $ε = ρ ε d - 1$ ，计算 $F (U d, x (t), ε) = 0$ 解得 $U d$ 令 $U ? = U d - 1$ ； $x 0 = x (t)$ ， $Δ x = x (t) - x (t - Δ t)$ ； $x ˙ (t) = Δ x / Δ t$ ； $d = d + 1$ ； $U ˉ ˙ = F D G M R E S (U, x (t), x ˙ (t), t, U ?, η m a x, ε)$ ； $U * = U d + U ˉ ˙ ? Δ t$ ；
步骤3	设置仿真时间 $t s i m$ ，输入初始状态 $x (t 0)$ ， $t 0 = 0$ ， $k = 0$ ， $w = 0.4$ ， $N = 20$ ， $Δ N = 5$
步骤4	当 $t p > Δ t$ ，令 $N = N + Δ N$ ；当 $t p < w Δ t$ ，令 $N = N - Δ N$ ；其他情况下， $N = N$ ；对初始状态 $x (t)$ 采样，计算状态量差值为： $Δ x = x (η Δ t) - x ((η - 1) Δ t)$
步骤5	通过算法（1）和（2）步骤得到最优控制序列 $U k *$ ，更新 $N$ 数值，计算得到控制规律 $u (γ a u x)$ ， $η = η + 1$ ， $t = η Δ t$ $t > t s i m$ 结束循环

参数	数值
车身质量 $m v$ / kg	1 560
质心到前轴的距离 $L f$ / m	1.156
质心到后轴的距离 $L r$ / m	2.035
转动惯量 $I z$ /（kg·m²）	1 536.7
轮胎模型形状因子 $C$	2.50
轮胎模型曲率因子 $E$	1.198

参数	数值
辨识系数 $k 1$	2.64× $105$
辨识系数 $k 2$	3.34× $105$
权重系数矩阵 $Q$	$105 ? d i a g {3 ? 3 ? 5 ? 5 ? 0 ? 0}$
权重系数矩阵 $R$	$105$
调整因子 $k a$	$3 / v x$
调整因子 $k b$	3.3

References 24

1	ZHOU X， YU X， ZHANG Y， et al. Trajectory planning and tracking strategy applied to an unmanned ground vehicle in the presence of obstacles［J］. IEEE Transactions on Automation Science and Engineering， 2021， 18（4）： 1575-1589.
2	潘世举，李华，苏致远，等. 基于跟踪误差模型的智能车辆轨迹跟踪方法［J］. 汽车工程， 2019， 41（9）： 1021-1027.
	PAN S J， LI H， SUN Z Y， et al. Trajeclory tracking method for intelligent vehicles based on tracking-error model［J］. Aulomotive Engineering， 2019， 41（9）： 1021-1027.
3	CHEN T， CHEN L， XU X， et al. Simultaneous path following and lateral stability control of 4WD-4WS autonomous electric vehicles with actuator saturation［J］. Advances in Engineering Software， 2019， 128： 46-54.
4	LIU W， WANG R， XIE C， et al. Investigation on adaptive preview distance path tracking control with directional error compensation［J］. Proceedings of the Institution of Mechanical Engineers， Part I： Journal of Systems and Control Engineering， 2020， 234（4）： 484-500.
5	CHATZIKOMIS C， SORNIOTTI A， GRUBER P， et al. Comparison of path tracking and torque-vectoring controllers for autonomous electric vehicles［J］. IEEE Transactions on Intelligent Vehicles， 2018， 3（4）： 559-570.
6	WU X， ZHOU B， WEN G， et al. Intervention criterion and control research for active front steering with consideration of road adhesion［J］. Vehicle system dynamics， 2018， 56（4）： 553-578.
7	李斯旭，徐彪，胡满江，等. 基于动力学模型预测控制的铰接车辆多点预瞄路径跟踪方法［J］. 汽车工程， 2021， 43（8）： 1187-1194.
	LI S X， XU B， HU M J， et al. A dynamic model predictive control approach for multipoint preview path tracking of articulated vehicles ［J］. Aulomotive Engineering， 2021， 43（8）： 1187-1194.
8	CHEN L， LIU M， SHI Y， et al. Adaptive fault estimation for unmanned surface vessels with a neural network observer approach［J］. IEEE Transactions on Circuits and Systems I： Regular Papers， 2021， 68（1）： 416-425.
9	FALCONE P， BORRELLI F， ASGARI J， et al. Predictive active steering control for autonomous vehicle systems［J］. IEEE Transactions on Control Systems Technology， 2007， 15（3）： 566-580.
10	SCHOLTE E， CAMPBELL M E. Robust nonlinear model predictive control with partial state information［J］. IEEE Transactions on Control Systems Technology， 2008， 16（4）： 636-651.
11	WAN Z， KOTHARE M V. Efficient scheduled stabilizing model predictive control for constrained nonlinear systems［J］. International Journal of Robust and Nonlinear Control： IFAC‐Affiliated Journal， 2003， 13（3‐4）： 331-346.
12	ARIENS D， HOUSKA B， FERREAU H， et al. Acado for matlab user’s manual［J］. Optimization in Engineering Center （OPTEC）， 2010， 1.
13	ZANON M， FRASCH J V， VUKOV M， et al. Model predictive control of autonomous vehicles［M］. Optimization and optimal control in automotive systems. Springer， Cham， 2014： 41-57.
14	DU X， HTET K K K， TAN K K. Development of a genetic-algorithm-based nonlinear model predictive control scheme on velocity and steering of autonomous vehicles［J］. IEEE Transactions on Industrial Electronics， 2016， 63（11）： 6970-6977.
15	ZHANG Y， KHAJEPOUR A， HASHEMI E， et al. Reconfigurable model predictive control for articulated vehicle stability with experimental validation［J］. IEEE Transactions on Transportation Electrification， 2020， 6（1）： 308-317.
16	GUO H， LIU F， XU F， et al. Nonlinear model predictive lateral stability control of active chassis for intelligent vehicles and its FPGA implementation［J］. IEEE Transactions on Systems， Man， and Cybernetics： Systems， 2017， 49（1）： 2-13.
17	TAVERNINI D， METZLER M， GRUBER P， et al. Explicit nonlinear model predictive control for electric vehicle traction control［J］. IEEE Transactions on Control Systems Technology， 2018， 27（4）： 1438-1451.
18	WANG Q， LIU Y， LIU H， et al. Parallel numerical continuation of periodic responses of local nonlinear systems［J］. Nonlinear Dynamics， 2020， 100（3）： 2005-2026.
19	AGOUJIL S， BENTBIB A H， JBILOU K， et al. A minimal residual norm method for large-scale Sylvester matrix equations［J］. Electronic Transactions on Numerical Analysis， 2014， 43： 45-59.
20	OHTSUKA T. A continuation/GMRES method for fast computation of nonlinear receding horizon control［J］. Automatica， 2003， 40（4）： 563-574.
21	GUO N， ZHANG X， ZOU Y， et al. A computationally efficient path-following control strategy of autonomous electric vehicles with yaw motion stabilization［J］. IEEE Transactions on Transportation Electrification， 2020， 6（2）： 728-739.
22	HU C， WANG R， YAN F， et al. Should the desired heading in path following of autonomous vehicles be the tangent direction of the desired path？［J］. IEEE Transactions on Intelligent Transportation Systems， 2015， 16（6）： 3084-3094.
23	BOYD S， BOYD S P， VANDENBERGHE L. Convex optimization［M］. Cambridge University Press， 2004.
24	SHEN C， BUCKHAM B， SHI Y. Modified C/GMRES algorithm for fast nonlinear model predictive tracking control of AUVs［J］. IEEE Transactions on Control Systems Technology， 2016， 25（5）： 1896-1904.

[1]	SHEN Zhe, WANG Yi-Gang, YANG Zhi-Gang, LI Fang-Xu. [J]. , 2016, 38(12): 1440 -1445 .
[2]	ZENG Bi-Qiang, GAO Ji-Dong, PENG Wei, SUN Zhen-Dong. [J]. , 2016, 38(12): 1446 -1451 .
[3]	LIU Hui, WANG Xiao-Jie, XIANG Chang-Le. [J]. , 2016, 38(12): 1483 -1487 .
[4]	PENG Qian-Lei, GUI Liang-Jin, FAN Zi-Jie. [J]. , 2016, 38(12): 1500 -1507 .
[5]	DONG Zhu-Rong, ZHANG Xin, HU Song-Hua, QIU Hao. [J]. , 2017, 39(1): 79 -85 .
[6]	SHI Hai-Min, YU Xiao-Li, LU Guo-Dong, HUANG Yu-Qi, LIU Zhen-Tao, HUANG Rui. [J]. , 2017, 39(1): 102 -106 .
[7]	QIN Chao-Ju, YANG Zhen-Zhong, ZHANG Wei-Zheng, SONG Li-Ye, YUAN Yan-Peng. [J]. , 2017, 39(2): 133 -137 .
[8]	ZHANG Guan-Jun, ZHAO Xin-Feng, CAO Li-Bo. [J]. , 2017, 39(2): 150 -158 .
[9]	HOU Tao, WEN Jing, KUANG Zhi-Peng, HE Yong-Yi, ZHANG Hai-Hong. [J]. , 2017, 39(2): 193 -199 .
[10]	WANG Bin, LI Tie, ZHANG Xiao-Qing, GUO Tao, SHI Qi. [J]. , 2017, 39(3): 256 -261 .

误差范围	improved-C/GRES/次	NMPC/次
［0，0.050）	11	0
［0.050，0.100）	35	0
［0.100，0.150）	4	35
［0.150，0.200）	0	8
［0.200，0.250）	0	6
［0.150，0.200）	0	1

误差范围	improved-C/GRES	NMPC
［0，0.100）	34	0
［0.100，0.200）	11	0
［0.200，0.300）	5	5
［0.300，0.400）	0	36
［0.400，0.500）	0	9

控制方法	仿真条件	平均计算时间/ms
improved--C/GMRES	工况1	18.9
GMRES	工况1	116.7
improved-C/GMRES	工况2	25.6
GMRES	工况2	132.8

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Research on Trajectory Tracking Control of Unmanned Vehicle Based on Efficient NMPC Algorithm

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References 24

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